Question

Question 8 8 pts The Earth takes slightly less than one day to complete one rotation about the axis passing through its poles. Assume that the actual time is 72976 seconds. Given this information, what is the angular speed of the Earth about its axis? Write your answer in rad/sec Question 9 8 pts A wheel with a 0.10-m radius is rotating at 35 rev/s. It then slows uniformly to 15 rev/s over a 9.92 - interval. What is the angular acceleration of a point on the wheel? Write your answer in rev per second squared (revis) Question 10 8 pts A certain merry-go-round is accelerated uniformly from rest and attains an angular speed of 1.2 rad/s in the first 12.16 seconds. If the net applied torque is 800 NX m, what is the moment of inertia (in kg.m of the merry-go-round?

Answer 1

Question 8 : The angular speed of the Earth about its axis which will be given by -

$\omega$ = (2$\pi$ rad) / T

$\omega$ = [(6.28 rad) / (72976 s)]

$\omega$ = 8.60 x 10^-5 rad/s

Question 9 : The angular acceleration of a point on the wheel which will be given by -

$\omega$_f = $\omega$₀ + $\alpha$ t

(15 rev/s) = (35 rev/s) + $\alpha$ (9.92 s)

[(15 rev/s) - (35 rev/s)] = $\alpha$ (9.92 s)

(-20 rev/s) = $\alpha$ (9.92 s)

$\alpha$ = [(-20 rev/s) / (9.92 s)]

$\alpha$ = - 2.01 rev/s²

Question 10 : If the net applied torque is 800 N.m, what is the moment of inertia of the merry-go-round?

using a rotational motion (i), we have

$\omega$_f = $\omega$₀ + $\alpha$ t

(1.2 rad/s) = (0 rad/s) + $\alpha$ (12.16 s)

$\alpha$ = [(1.2 rad/s) / (12.16 s)]

$\alpha$ = 0.0986 rad/s²

We know that, $\tau$ = I $\alpha$$\Leftrightarrow$ I = $\tau$ / $\alpha$

I = [(800 N.m) / (0.0986 rad/s²)]

I = 8113.5 kg.m²

Question 11 : The pressure acting on the treasure chest which will be given by -

P = _$\rho$water g h

P = [(1000 kg/m³) (9.8 m/s²) (17 m)]

P = 166600 Pa

We know that, P_absolute = P_atmospheric + P_water

P_absolute = [(1 x 10⁵ Pa) + (166600 Pa)]

P_absolute = 266600 Pa

What is the magnitude of the force that acts on the rectangular top?

F = P_absolute A

F = (266600 Pa) [(0.5 m) (1 m)]

F = 133300 N

Question 12 : What volume does 7.49 kg of carbon dioxide occupy at standard temperature and pressure?

we know that, V = m / _$\rho$

V = [(7.49 kg) / (1.98 kg/m³)]

V = 3.78 m³

Question 13 : If the radius of a piston is 0.69 m, what is the maximum mass that can be raised using this piston?

using a formula, we have

F = P A = (4 x 10⁵ Pa) ($\pi$ r²)

F = [(4 x 10⁵ Pa) (3.14) (0.69 m)²]

F = 597981.6 N

we know that, F = m a

m = [(597981.6 N) / (9.8 m/s²)]

m = 61018.5 kg